No, it's not a Zebra. It's a zebra shark.
I was pursuing the way of the barcode already, but thanks to @elias comment, it became crystal clear that the 1 and 0 were to be composed in a barcode.
First attempt:
I put together the 1 as black stripes and 0 as white stripes but it didn't work. http://www.onlinebarcodereader.com/ (and a bunch of other online barcode readers didn't read anything)
Second attempt:
I tried viceversa and voilà. Reading it using http://www.onlinebarcodereader.com/ we get the word (not yet meaningful) Zebedee. Link to the fiddle used to prepare the barcode: https://jsfiddle.net/cfk43z5v/1/
Now, with the help of Google:
After digging into the Bible character Zebedee, a simple googling of "zebedee zebra" led me to the extraordinary zebra shark (bbc and national geographic) that had a virgin birth. Now, I can't believe I'm on a wrong way and that this is just a coincidence. I think that's a zebra shark!!
Edit: as the OP pointed out below, the same google search leads to the zebra Zebedee. So I must say that it's also an actual zebra!!